Trapped surface formation for the Einstein-Scalar system
Dr. Peng Zhao
2023-02-09 20:00-21:30
Online
Speaker: Dr. Peng Zhao (Beijing Normal University, Zhuhai)Time: 20:00-21:30 February 9, 2023 (Thursday)
Title: Trapped surface formation for the Einstein-Scalar system
Abstract: We consider a massless scalar field minimally coupled to gravity. We show that the focussing of gravitational wave and scalar field lead to the trapped surface formation without symmetries. This paper follows An's strategy in the trapped surface formation of pure gravity and Einstein-Maxwell system to study a characteristic initial value problem (CIVP) for the Einstein-Scalar system with the initial data given on two intersecting null hypersurfaces, the incoming one of which is Minkowskian and the outgoing one of which is assumed without symmetries. We obtain a scale–critical semi-global existence result by assigning the signature for decay rates to both geometric quantities and scalar field. In the analysing we make use of a gauge due to J. Stewart and an adjustment to the Geroch-Held-Penrose (GHP) formalism, the T-weight formalism which reveals the deep relations between Newman-Penrose (NP) quantities and PDE analysis.
